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2009, 113, 9023–9028
Published on Web 05/04/2009
Measuring the Optical Absorption Cross Sections of Au-Ag Nanocages and Au Nanorods
by Photoacoustic Imaging
Eun Chul Cho,†,| Chulhong Kim,†,| Fei Zhou,‡ Claire M. Cobley,† Kwang Hyun Song,†
Jingyi Chen,† Zhi-Yuhan Li,‡ Lihong V. Wang,*,† and Younan Xia*,†
Department of Biomedical Engineering, Washington UniVersity, St. Louis, Missouri 63130, and Laboratory of
Optical Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, China
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ReceiVed: April 10, 2009; ReVised Manuscript ReceiVed: April 23, 2009
This paper presents a method for measuring the optical absorption cross sections (σa) of Au-Ag nanocages
and Au nanorods. The method is based on photoacoustic (PA) imaging, where the detected signal is directly
proportional to the absorption coefficient (µa) of the nanostructure. For each type of nanostructure, we first
obtained µa from the PA signal by benchmarking against a linear calibration curve (PA signal versus µa)
derived from a set of methylene blue solutions with different concentrations. We then calculated σa by dividing
the µa by the corresponding concentration of the Au nanostructure. Additionally, we obtained the extinction
cross section (σe, sum of absorption and scattering) from the extinction spectrum recorded using a conventional
UV-vis-NIR spectrometer. From the measurements of σa and σe, we were able to easily derive both the
absorption and scattering cross sections for each type of gold nanostructure. The ratios of absorption to
extinction obtained from experimental and theoretical approaches agreed well, demonstrating the potential
use of this method in determining the optical absorption and scattering properties of gold nanostructures and
other types of nanomaterials.
Introduction
Due to their unique optical properties, Au-based nanostructures have received considerable attention in biomedical applications as both diagnostic contrast agents and therapeutic
agents.1,2 Gold-based nanostructures can interact with incident
light and give rise to a strong extinction peak in the visible and
near-infrared (NIR) regions.3 This extinction peak is known as
the localized surface plasmon resonance (LSPR), which consists
of two components, scattering and absorption. By manipulating
the size, shape, and internal structure (solid versus hollow) of
the nanostructures, one can tune not only the position and
intensity of the peak but also the relative magnitude of light
being absorbed or scattered.4-7 The magnitude of light being
absorbed or scattered is determined by the absorption and
scattering cross sections (σa and σs, respectively) of the
nanostructures. In general, different applications may require
nanostructures having specific optical properties. For example,
while Au-based nanostructures with relatively large σs are ideal
for enhancing the contrast of optical coherence tomography
(OCT),8 photoacoustic (PA) imaging requires contrast agents
with relatively large σa.9 Similarly, the nanostructures must have
a large σa in order to effectively convert the incident light into
heat for photothermal therapy.10 Therefore, it is essential to know
both the σa and σs of a nanostructure for a specific biomedical
application.
* To whom correspondence should be addressed. E-mail: lhwang@biomed.
wustl.edu (L.V.W., photoacoustics); [email protected] (Y.X., Au
nanostructures).
†
Washington University.
‡
Chinese Academy of Sciences.
|
These two authors contributed equally to this work.
10.1021/jp903343p CCC: $40.75
A conventional UV-vis-NIR spectrometer can be used to
easily record the extinction spectra of nanostructures. Using the
Beer-Lambert law,11 one can obtain the molar extinction
coefficient and thus the extinction cross section (σe, with σe )
σa + σs) of the nanostructures. In general, one has to rely on
theoretical calculation in order to separate σe into σa and σs. In
this regard, the Mie theory12 works perfectly for spherical
particles, while the discrete-dipole approximation (DDA) is wellsuited for nanostructures with other geometric shapes.13-16
Experimentally, a number of groups have tried to measure the
σa of aquatic particles with integrating spheres in a dual-beam
configuration.17 Others have attempted to use OCT to quantify
the backscattered light of gold nanostructures and then derive
the σa using a numerical model.18 In an early study, Rossler
and Faxvog tried to obtain the ratio of optical absorption to
extinction for aerosols by simultaneously monitoring photoacoustic signals and light attenuation in a small chamber
containing cigarette smoke.19 They also compared their experimental data with the results obtained from theoretical calculations. For gold and other metal nanostructures, they are typically
dispersed in water so that one must design a different system
for measuring the optical absorption.
In this study, we experimentally measured the σa of Au-Ag
nanocages and Au nanorods using a PA imaging system, a
hybrid imaging modality that can provide strong optical
absorption contrast and high ultrasonic resolution. This technique
can provide three-dimensional images of optical absorption
heterogeneities in biological tissue in vivo.9,20 It is known that
the PA signal is generated due to the optical absorption of a
material, and the signal is expected to be directly proportional
to the absorption coefficient (µa) of the material within a certain
 2009 American Chemical Society
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J. Phys. Chem. C, Vol. 113, No. 21, 2009
Letters
Figure 1. Extinction coefficients (µe) of nanostructures. (A) Au-Ag nanocages of 45.0 nm in outer edge length and 5.8 nm in wall thickness, at
a concentration of 0.13 nM; (B) Au-Ag nanocages of 32.0 nm in outer edge length and 4.0 nm in wall thickness, at a concentration of 0.33 nM;
(C) Au nanorods of 44 nm × 19.8 nm in length × width, at a concentration of 0.56 nM; and (D) Au nanospheres of 150 nm in diameter, at a
concentration of 1.42 pM. The insets show corresponding TEM images.
concentration range.21,22 On the basis of this principle, we could
convert the PA signal from a sample of the nanostructures into
the µa by benchmarking against a linear calibration curve based
on an organic dye (e.g., methylene blue) that describes the
relationship between the PA signal and the µa. Then, we could
acquire σa by dividing µa by the concentration of the nanostructure. When combined with the conventional UV-vis-NIR
spectroscopic method, we could experimentally determine the
σe, σa, and σs of the Au-based nanostructure.
Experimental Methods Section
Preparation of Au Nanostructures. Four types of nanostructures were evaluated in this study, Au-Ag nanocages with
two different sizes, Au nanorods, and Au nanospheres. Figure
1 shows their extinction coefficients (µe) and TEM images
(insets). Their corresponding chemical compositions and geometric parameters are provided in the Supporting Information
(Table S1). The two types of Au-Ag nanocages (45 and 32
nm in outer edge length, respectively) were prepared by titrating
the corresponding Ag nanocubes with 1 mM HAuCl4.7b Once
the LSPR peak had reached 650 nm, addition of HAuCl4 was
immediately stopped. The Au nanorods (44.0 × 19.8 nm2 in
length × width) were synthesized using the method developed
by El-Sayed and co-workers.23 The longitudinal LSPR peak of
the Au nanorods was tuned to 650 nm. The Au nanospheres
(∼150 nm in diameter) were purchased as an aqueous suspension from Ted Pella. They exhibited a very broad LSPR peak
at around 650 nm due to the involvement of multipole
excitations. An organic dye, methylene blue (MB), was used
as a reference for calibration because its molar absorption
coefficient is well documented.24
PA Imaging System. Figure 2A shows a setup of the PA
imaging system used for the optical measurements. The principle
of this dark-field illumination PA imaging system can be found
elsewhere.10b,22 A wavelength-tunable dye laser (ND6000,
Continuum), pumped by a Q-switched Nd:YAG laser (LS-2137,
Figure 2. (A) An experimental setup of the photoacoustic (PA)
imaging system. (B) A typical depth-resolved B-scan PA image (x-z
scan) of the Au-Ag nanocage suspension (45.0 nm in outer edge length,
Figure 1A) at three different concentrations.
LOTIS), produced laser pulses with <15 ns pulse widths at a
rate of 10 Hz; 5% of the energy of each pulse was split from
the laser beam, measured by a photodiode, and used to
compensate for the fluctuation of pulse energy. A ring-shaped
illumination (λ ) 638 nm) was formed by a concave and conical
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Letters
J. Phys. Chem. C, Vol. 113, No. 21, 2009 9025
lenses. The light traveling down through an optical condenser
and the ultrasound focal zone were focused on the Au nanostructures. We used an optically scattering medium to prevent
direct illumination of the sample by light, protecting the Au
nanostructures and MB molecules from deformation and photobleaching, respectively. Three Tygon tubes were embedded
in the optically scattering medium, and the tubes were then filled
with aqueous suspensions of the Au nanostructures or aqueous
solutions of MB. When the solution was illuminated by the laser,
PA waves were generated through thermoelastic expansion due
to optical absorption. The PA waves were detected by a singleelement 5 MHz ultrasound transducer (V308, Panametrics-NDT)
placed inside of the optical condenser. The PA signals were
collected, amplified, and then transferred to an oscilloscope. The
spatial resolutions of this PA imaging system were 138 µm in
the axial direction and 490 µm in the transverse direction. We
obtained depth-resolved (z-direction) one-dimensional images
(A-lines) by measuring the arrival times of the PA signals. By
scanning along the x direction, we can obtain two-dimensional
PA image (B-scan). Figure 2B shows a typical depth-resolved
B-scan PA image of the Au-Ag nanocages shown in Figure
1A with concentrations at 0.13, 0.07, and 0.03 nM. The PA
signal decreased in amplitude as the concentration of nanocages
was reduced. For each data point, we obtained 20 B-scan images
from the same solution by scanning samples along the ydirection, and the PA signals were averaged from the images.
Figure 3. Plots of PA signal amplitude versus concentration for three
types of nanostructures. No PA signal was detected from the suspension
of Au nanospheres under the experimental conditions.
Results and Discussion
The PA signal measured from a material is related to µa
(cm-1) according to the following equation22
P0 ) ΓµaF
(1)
where P0 is the initial photoacoustic pressure due to laser
excitation, Γ is the Grueneisen parameter, and F is the optical
fluence. Γ and F are determined by the properties of the medium
and the incident light. Since we used the same scattering medium
and a single wavelength, Γ and F were essentially the same for
all experiments. Therefore, the PA signal was directly proportional to µa of the light-absorbing species.
For simplicity in data analysis, it is important to determine
the concentration range in which there is a linear relationship
between the PA signal and the concentration of the dye
molecules or nanostructures. As a control experiment, we
measured the PA signal by filling the tube with deionized water,
and a value of 0.55 au was detected. We then measured the PA
signals of the reference dye, MB, and we found that the PA
signals linearly increased to 1.1 au (62.5 µM) as the concentration of MB was increased (Figure S1, Supporting Information),
and then, the signals became saturated. In Figure 3, we plot the
PA signal as a function of the nanostructure concentration for
the two types of Au-Ag nanocages and Au nanorods. In all
cases, the PA signal increased linearly as the concentration of
nanostructures was increased. We could not detect any PA signal
from the suspension of Au nanospheres up to a concentration
of 50 pM, at which point, the aqueous suspension started to
show an opaque appearance (probably due to particle agglomeration).
We next tried to acquire the absorption coefficients of the
nanostructures (µa,nano). To directly calculate µa,nano from eq 1,
we need to know Γ and F, two parameters that are difficult to
measure experimentally. We came up with a suitable way to
acquire µa,nano by using a calibration curve derived from the
linear relationship between the PA signal and µa for MB
solutions at various concentrations. In this case, we first
Figure 4. The linear relationship between the optical absorption
coefficient (µa) and PA signal amplitude derived from the plot in Figure
S1 and the known σa of methylene blue (R2 ) 0.99).
measured the PA signals from aqueous solutions of MB at
various concentrations (see Figure S1, Supporting Information)
and then plotted the µa against the PA signal to derive the linear
correlation (Figure 4). We calculated µa from the molar
absorption coefficient at 638 nm.24 The linear dependence in
Figure 4 can be described using the following empirical equation
µa ) 11.99 × PA signal - 5.92
(2)
After obtaining µa,nano for the nanostructures from eq 2 at the
concentrations shown in Figure 3, we calculated their absorption
cross sections using the following equation22
µa,nano ) Nnanoσa,nano
(3)
2
where σa,nano is the absorption cross section (m ) and Nnano is
the concentration of the nanostructure (number of particles per
m3).
We also obtained the extinction coefficients of the four types
of nanostructures from their UV-vis-NIR spectra and the
Beer-Lambert law (see Figure S2, Supporting Information).
Table 1 summarizes the extinction (σe,nano) and absorption
(σa,nano) cross sections of the nanostructures. To validate our
experimental approach, we compared our experimental data with
calculation results. Figure 5 shows the spectra calculated for
individual particles of the four types of nanostructures. The
LSPR peaks of all of these nanostructures were located at 650
nm. In calculation, the elemental compositions of Au-Ag
nanocages and all of the geometrical data (see the insets of
Figure 5) were determined experimentally by EDX and TEM
analysis. For the Au nanosphere, calculation was performed by
Mie theory,12 while calculations for the Au-Ag nanocages and
the Au nanorods were carried out using the DDA method.13-16
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J. Phys. Chem. C, Vol. 113, No. 21, 2009
Letters
TABLE 1: Comparison of the Optical Cross Sections of Au-Based Nanostructures Obtained Experimentally by Photoacoustic
Imaging and Theoretical Calculationa
cross section (10-15 m2)
nanocages (45.0 nm)
experimental
calculated
experimental
calculated
experimental
calculated
experimental
calculated
nanocages (32.0 nm)
nanorods (44.0 × 19.8 nm2)
nanospheres (150 nm)
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a
extinction (σe)
absorption (σa)
σa/σe
7.26 ( 0.06
19.88
2.99 ( 0.04
6.39
2.16 ( 0.02
2.15
145 ( 14.76
99.96
5.96 ( 0.25
16.26
3.05 ( 0.12
6.02
1.87 ( 0.23
1.83
b
5.73
0.82 ( 0.04
0.82
1 ( 0.04
0.94
0.87 ( 0.11
0.85
0.056
b
All the values were obtained at 638 nm. Not detected with photoacoustic imaging.
Figure 5. Spectra calculated for (A) Au-Ag nanocages with an outer edge length of 45.0 nm and wall thickness of 5.8 nm; (B) Au-Ag nanocages
with an outer edge length of 32.0 nm and wall thickness of 4.0 nm; (C) Au nanorods of 44.0 and 19.8 nm in length and width, respectively; and
(D) Au nanospheres of 150 nm in diameter. For the Au-Ag nanocages and Au nanorods, the discrete dipole approximation (DDA) method was
used, and the Mie theory was used for the Au nanospheres. The inset shows the corresponding geometric parameters for each type of gold-based
nanostructure. Abbreviation: ext. ) extinction; abs. ) absorption; sca. ) scattering.
For the Au-Ag nanocages, the electric field was set along [100],
and the calculation used a dielectric function modified by
considering electron surface scattering.14 As shown in the insets,
we assumed that the nanocages had a cubic shape. For the Au
nanorod, the electric field (e-field) was set with a direction of
65° from the long axis. The rod was assumed to take a square
cross section with the corners slightly rounded with a radius of
6.1 nm.
From Table 1, it is apparent that the ratios of absorption to
extinction cross sections (σa/σe) obtained from experimental and
theoretical approaches agreed well. Each type of nanostructure
has its own characteristic σa/σe ratio, which is essentially the
same as that predicted by calculation. This agreement demonstrates the practical value of our experimental approach, which
can be used to quickly measure the absorption and scattering
cross sections of Au-based nanostructures. There are some
discrepancies in absolute units between the experimentally
measured and calculated values of σa and σe for both Au-Ag
nanocages. These discrepancies might have been caused by
factors such as variations in size, shape, and wall thickness in
the actual sample, as well as pores that were often found in the
surface of small Au-Ag nanocages (see the inset in Figure 1B).
These parameters can affect the concentrations of Au nanostructures determined by inductively coupled mass spectroscopy
(ICP-MS). Despite these discrepancies, the experimental data
can still be employed to validate the effect of size and geometric
shape of nanostructures on their optical properties.
When comparing the optical properties of the two types of
Au-Ag nanocages, we found that the smaller nanocages had a
higher σa/σe ratio, while the absolute value of σa is larger for
the larger nanocages. This finding agrees with the previous
results in that small Au-Ag nanocages had smaller extinction
cross sections than the larger counterparts and that optical
absorption became more significant as the dimensions of
Au-Ag nanocages were reduced.2b,25 As explained above,
however, the absolute values of the calculated extinction and
absorption cross sections are 2.7 and 2.1 times the experimental
data for 45 and 32 nm Au-Ag nanocages, respectively. In the
present work, we used 45 nm Au-Ag nanocages consisting of
a Au-Ag alloy for the walls and some pure Ag in the interior
(see the inset in Figure 1A), while we only considered a Au-Ag
alloy for the walls in our DDA calculations. Along with
variations in size and wall thickness of the Au-Ag nanocages,
this simplification might result in some differences for the
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Letters
absolute values. In addition, the 32 nm Au-Ag nanocages that
we used in our experiments were rather deviated from a cubic
shape, and some cages had pores in the side faces. Our
calculation results from the 32 nm nanocages indicate that corner
truncation tends to reduce both σa and σe, while a similar σa/σe
ratio is maintained (see Figure S3, Supporting Information). For
the effect of pores, it was reported that the formation of pores
could decrease the absolute values while the peak positions are
maintained.25
For the Au nanorods, both the experimental data and
calculation results were almost the same. The σa/σe ratio of the
Au nanorods was found to be between those for the 45 and 32
nm Au-Ag nanocages. On the other hand, the absolute values
of σa and σe for the Au nanorods were smaller than those for
both samples of Au-Ag nanocages. This might be due to the
fact that the Au nanorods have two peaks in the spectra, a
longitudinal mode at 650 nm and a transversal mode at 520
nm. In our calculations, we assumed that the Au nanorod was
aligned in a diagonal manner with an angle of 65° between the
long axis and the e-field in order to generate the two peaks. If
we consider only the longitudinal mode, or by aligning the Au
nanorod perpendicular to the incident beam or the long axis
parallel to the e-field, σa and σe were increased to 9.9 × 10-15
and 11.6 × 10-15 m-2 (σa /σe ) 0.85), respectively (Figure S4,
Supporting Information). The round corners of the Au nanorods
(see inset in Figure 1C) could also cause reduction for the cross
sections. It is known that sharp corners tend to form a strong
dipole, giving the metal nanorod a larger cross section.15 A
recent calculation studied the effect of the geometric shape of
a Au nanorod on its optical cross section, and σe was found to
increase as the shape of the Au nanorod became more
rectangular.16,26 As in the case of Au-Ag nanocages, the size
of the Au nanorods influenced both the absolute values of the
cross sections and the σa/σe ratio. Lee and El-Sayed reported in
their calculations that increasing the size of the Au nanorod
with a fixed aspect ratio resulted in a decrease in σa while σe
remained almost constant.16
We attribute the lack of PA signals from the Au nanospheres
to the low absorption at 638 nm. In our calculation, σa was 5.7%
of σe for the Au nanospheres at this wavelength; therefore, a
much higher concentration was required for the Au nanosphere
suspension in order to detect the PA signals. Unfortunately, as
we stated above, we found that the Au nanospheres became
opaque at 50 pM probably due to particle aggregation. The
extinction spectra taken from the suspensions of Au nanospheres
supported this claim as the extinction coefficient at 638 nm was
nonlinearly increased above a concentration of 5.7 pM and
became saturated at 50 pM (see Figure S5, Supporting Information). A concentration of Au nanospheres higher than 50 pM is
needed in order to detect PA signals at 638 nm, but we could
not prepare such a sample for the aforementioned reason.
Although we could not detect PA signals at this wavelength,
we believe it is possible to detect PA signals from the Au
nanospheres if we use a laser with a different wavelength (e.g.,
at 530 nm). At this wavelength, the Au nanospheres have a
fairly high σa/σe ratio (0.44).
Conclusion
We have demonstrated a method based on photoacoustic
imaging for measuring the absorption cross sections of Au-based
nanostructures. Using the calibration curve between PA signals
and the absorption coefficients of MB solutions, we could
convert the PA signal from an aqueous suspension of Au
nanostructures into the absorption coefficient and further derive
J. Phys. Chem. C, Vol. 113, No. 21, 2009 9027
the absorption cross section. Combining this method with
conventional UV-vis-NIR spectroscopy, we have determined
both the absorption and scattering cross sections of Au-Ag
nanocages and Au nanorods. In this study, we found that the
geometric parameters (including size and shape) of the Au
nanostructures can have a strong influence on their cross sections
and σa/σe ratios; and the nonuniformity in geometric parameters
can sometimes cause a deviation for the absolute values of cross
sections obtained experimentally by PA imaging from those
obtained by calculation. We believe this approach is extendable
to other types of metal nanostructures or Au-based nanostructures with LSPR peaks being tuned to other spectral regions.
We recommend using MB as a reference dye to obtain the
calibration curve if the LSPR peaks of the nanostructures are
located in the range of 600-680 nm. For other spectral regions,
we need to use other dyes with appropriate absorption peak
positions to construct the calibration curves. For example, we
have recently found that indocyanine green (ICG) is useful as
a reference dye when the LSPR peaks of Au-Ag nanocages or
Au nanorods are tuned to 800 nm. This method can help us
better understand the optical properties of various metal
nanostructures and thus have them optimized for different
applications.
Acknowledgment. This work was supported, in part, by
grants from National Institutes of Health (R01 EB000712, R01
EB008085, R01 NS46214, and U54 CA136398sthe Network
for Translational Researchsto L.V.W.). L.V.W. has a financial
interest in Endra, Inc., which, however, did not support this
work. Y.X. thanks the National Institutes of Health for a 2006
Director’s Pioneer Award (DP1 OD000798-04). Z.Y.L. was
supported by the National Natural Science Foundation of China
(60736041 and 10874238). E.C.C. was also partially supported
by a fellowship from the Korea Research Foundation (KRF2007-357-D00070) funded by the Korean Government.
Supporting Information Available: Physical and chemical
parameters and additional results. This material is available free
of charge via the Internet at http://pubs.acs.org.
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JP903343P
Supporting Information
Measuring the Optical Absorption Cross-sections of Au-Ag Nanocages and
Au Nanorods by Photoacoustic Imaging
Eun Chul Cho,†,∥ Chulhong Kim, †,∥Fei Zhou,‡ Claire M. Cobley,† Kwang Hyun Song,†
Jingyi Chen,† Zhi-Yuhan Li,‡ Lihong V. Wang,†,* and Younan Xia†,*
†
Department of Biomedical Engineering, Washington University in St. Louis, Missouri 63130.
‡
Laboratory of Optical Physics, Institute of Chinese Academy of Sciences, Beijing 100080
China.
*Corresponding authors. E-mail: Lihong V. Wang: [email protected]
Younan Xia: [email protected]
∥
These authors contributed equally to this work.
S1
Table S1. Physical and chemical parameters of Au-based nanostructures shown in Figure 1.
Atomic composition (%)a
Nanostructures
a
Au
Ag
Fig. 1A
Nanocages
21
79
Fig. 1B
Nanocages
27
73
Fig. 1C
Nanorods
100
0
Fig. 1D
Nanospheres
100
0
Dimensionsb
Outer length: 45.0 ± 7.1 nm
Wall thickness: 5.8±1.1 nm
Outer length: 32.0 ± 4.9 nm
Wall thickness: 4.0 ± 1.2 nm
Length: 44.0 ± 7.9 nm
Width: 19.8 ± 6.5 nm
Diameter: 150 ± 17 nm
The atomic compositions of the nanocages were obtained by energy-dispersive X-ray
spectroscopy (EDX).
b
All dimensions were estimated based on TEM images.
S2
Figure S1. A plot of the PA amplitude against the concentration of methylene blue.
S3
Figure S2. Plots of the extinction coefficient (µe) at 638 nm against the concentrations of Aubased nanostructures, where the extinction spectra were recorded using a conventional UVvis-NIR spectrometer. (A) Au-Ag nanocages (outer edge length 45.0 nm, wall thickness 5.8
nm), (B) Au-Ag nanocages (outer edge length 32.0 nm, wall thickness 4.0 nm), (C) Au
nanorods (44.0 × 19.8 nm2 in length × width), and (D) Au nanospheres (150 nm in diameter).
From these values, the optical extinction cross sections were obtained using the Beer-Lambert
law.
S4
Figure S3. Calculated cross sections of the Au-Ag nanocages (32 nm in outer edge length and
4 nm in wall thickness) with 6-nm snipped corners. The extinction and absorption cross
sections at 638 nm are 5.39×10-15 and 5.11×10-15 m2, respectively, and the ratio of absorption
to extinction cross sections is 0.95. The inset shows the corresponding geometry used for the
calculation. Abbreviation: ext.= extinction; abs.= absorption; sca.= scattering.
S5
Figure S4. Calculated cross sections of the Au nanorod (44 × 19.8 nm2 in length × width)
with corners rounded when the Au nanorod is aligned perpendicular to the incident beam. The
extinction and absorption cross-sections at 638 nm are 9.9×10-15 and 11.6×10-15 m-2,
respectively, and the ratio of absorption to extinction cross sections is 0.85. Abbreviation:
ext.= extinction; abs.= absorption; sca.= scattering.
S6
Figure S5. (A) Optical extinction coefficient (µe) of the Au nanospheres (150 nm in diameter)
at various concentrations. (B) A plot of µe against the concentration of the Au nanospheres at
638 nm.
S7